T-Mobile USA’s deal yesterday to buy 4G spectrum covering 60 million people will help it compete nationally in the wireless game — but it won’t give it a boost locally because it didn’t include any New York City airwave licenses, a source close to the situation said.

“They would have loved to have had New York spectrum,” the source noted.

T-Mobile caved in at the end because it felt it got as much as it could from Verizon Wireless — which handed over the valuable 4G spectrum in exchange for licenses covering 22 million people, plus cash, sources said.

Verizon’s deal with T-Mobile was made with an eye toward winning regulatory approval of its $3.6 billion spectrum purchase from a Comcast-led group of cable companies.

Verizon and the cable companies will also enter into a joint-marketing program under the deal.

T-Mobile opposed the Verizon-Comcast deal.

Without yesterday’s deal with Verizon, T-Mobile claimed it couldn’t compete in the 4G game.

Now, according to a spokesman for the company, “T-Mobile plans to launch [4G] LTE in 2013 and expects to reach more than 200 million Americans with [4G] LTE by the end of 2013.”

Regulators last year blocked AT&T’s acquisition of T-Mobile, believing consumers needed three strong national cellular carriers.

Former Federal Communications Commission Chair Reed Hundt told The Post, “I think this is a win-win-win-deal. It’s very good for T-Mobile, fine for Verizon because it will be able to close its deal, and good for the country.”

The Post reported exclusively in May that the FCC was weighing requiring Verizon to sell valuable 4G spectrum in 12 markets to complete its deal. Yesterday’s Verizon deal covers 15 markets, but not the prized Big Apple.

FCC Chair Julius Genachowski, a source said, did not care in which markets Verizon sold spectrum.